1. ## metric space

Hi , i have this problem , i need help with this exercise

If b $\displaystyle \notin$ B[a,r] , prove that exist s>0 such that B[a,r] $\displaystyle \cap$ B[b,s] = $\displaystyle \emptyset$

Thanks

2. ## Re: metric space

Originally Posted by resident911
Hi , i have this problem , i need help with this exercise
If b $\displaystyle \notin$ B[a,r] , prove that exist s>0 such that B[a,r] $\displaystyle \cap$ B[b,s] = $\displaystyle \emptyset$
Please, please get in the habit of posting the meaning of notations that you use.
If $\displaystyle B[a,r]=\{x:d(a,x)<r\}$ the ordinary ball then the statement is false.
If $\displaystyle B[a,r]=\{x:d(a,x)\le r\}$ the ordinary closed ball then the statement is true.
Which is it? Or is it something altogether different?